Which of the following numbers is a factor of 176? ${5,7,8,13,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $176$ by each of our answer choices. $176 \div 5 = 35\text{ R }1$ $176 \div 7 = 25\text{ R }1$ $176 \div 8 = 22$ $176 \div 13 = 13\text{ R }7$ $176 \div 14 = 12\text{ R }8$ The only answer choice that divides into $176$ with no remainder is $8$ $ 22$ $8$ $176$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $176$ $176 = 2\times2\times2\times2\times11 8 = 2\times2\times2$ Therefore the only factor of $176$ out of our choices is $8$. We can say that $176$ is divisible by $8$.